Finite Element Analysis for Engineering Design

From the preface: "The advent of computers has opened new horizons in the field of engineering design. In the realm of analysis for engineering design the finite element method has emerged as a powerful tool for modeling and analysis of solids and structures of complex geometries and variable material properties in many areas of engineering design such as machine components, pressure vessels, nuclear reactors, off-shore structures, steel and concrete buildings, bridges, towers, automobile components, turbine parts, power plant structures, etc. The text-book literature on the finite element method exists at an introductory level through the new and more advanced level of simple applications. Modeling and analysis of practical problems continue to be developed and published in technical journals. Developments are also taking place in the use of artificial intelligence techniques in expert systems to advise the analysts on the choice of the elements, type of analysis, discretization, etc. for solving complicated problems. It is essential to periodically synthesize all the developments on the finite element method and its applications to practical problems of engineering design and also to identify the future areas of research both in the domains of academic research and industrial applications. Keeping this in mind an advanced study institute was organized at Indian Institute of Technology, Madras, India during Aug. 1-10, 1988. This volume contains lecture notes prepared by the invited lecturers attending the Advanced Study Institute. It should serve as a ready reference to researchers and practitioners engaged in the finite-element analysis related to engineering design in several disciplines."

1. A Review of the Equations of Mechanics.- Classification of Equations.- Descriptions of Motion.- Strains and Strain-Displacement Relations.- Compatibility Equations.- Stress and Equations of Motion and Equilibrium.- Constitutive Relations.- Equations of Linear Elasticity.- Biographical Sketch.- 2. Variational Formulations and Methods.- The Variational Operator.- Principle of Virtual Displacements.- The Principle of Virtual Forces.- Incremental Variational Formulations of Nonlinear Problems.- Variational Methods of Approximation.- 3. An Introduction to the Finite Element Method.- One-Dimensional Problems.- Two-Dimensional Problems.- Closure.- 4. Interpolation, Simple Elements, Convergence, Stress Calculation.- A Piecewise Polynomial field.- Finite Element Form of the Rayleigh-Ritz Method.- Interpolation.- Shape Functions for C0 Elements.- Shape Functions for C1 Elements.- Formulas for Element Matrices [k] and {re}.- Overivew of Element Stiffness Matrices.- Consistent Element Nodal Loads {re}.- Equilibrium and Compatibility in the Solution.- Convergence Requirements.,.- The Patch Test.- Stress Calculation.- References.- Symbols.- Biographical Sketch.- 5. The Isoparametric Formulation.- An Isoparametric Bar Element.- Plane Bilinear Isoparametric Element.- Summary of Gauss Quadrature.- Computer Subroutines for the Bilinear Element.- Quadratic Plane Elements.- Hexahedral (Solid) Isoparametric Elements.- The Validity of Isoparametric Elements.- Appropriate Order of Quadrature.- Element and Mesh Instabilities.- Remarks on Stress Computation.- Examples. Effect of Element Geometry.- References l58.- 6. Constraints.- Constraints. Transformations.- Lagrange Multipliers.- Penalty Functions.- Naturally Arising Penalty Formulations. Numerical Integration and Constraints.- Constraint Counting.- References.- 7. Remarks About Modeling.- References.- 8. Three-Dimensional Finite Element Models.- 3-D Solid Elements.- Eight-Noded Isoparametric Element.- Twenty-Noded Isoparametric Element.- Element Load Vector.- Computation of Stresses.- 30 Solid Elements for Concrete Structures Analysis.- Applications.- References.- 9. Geometric Nonlinear Analysis of Framed Structures.- Strain-Displacement Relationship.- Types of Formulation/Coordinate Systems.- Generalized Approach - Total Lagrangian Formulation.- Case Studies and Discussion.- Discussion.- References.- 10. Two-Dimensional Theories of Plates.- A Review of Literature.- Classical and First-Order Plate Theories.- Mixed Formulation of the Third-Order Theory.- Moderate Rotation Plate Theories.- References.- 11. Solution of Nonlinear Equations.- Governing Equations.- Solution Procedures.- Newton-Like Methods.- Accelerators and Line Search.- References.- 12. Dynamics of Structures: Fundamentals.- Finite Element Formulation.- Modal Analysis.- Structural Damping.- Consistent and Lumped Mass Models.- References.- 13. Dynamics of Structures: Solution Techniques.- Solution of First-Order Parabolic Systems.- Solution of the Structural Dynamics Equations.- Recent Developments in Time Integration 33l.- References.- 14. Mechanics of Composite Structures.- Definitions and Terminology.- Stress-Strain Relations for Laminates.- Classical and First-Order Laminate Theories.- Special Cases of Lamination Schemes.- A General Laminate Plate Theory.- References.- 15. Analysis Of Laminated Composite Structures.- Analytical Solutions of Classical and First-Order Theories.- Analytical Solutions of the Third-Order Theory.- Analytical Solutions of the Generalized Laminate Theory.- Finite-Element Models of 2-D Plate Theories.- Degenerate 3-D Composite Shell Element Based on the Total Lagrangian Formulation.- References.- 16. Applications of the Finite Element Method in Geotechnical Engineering.- Soil-Structure Interaction Problems.- Earth and Rock-Fill Dam.- Foundation of a Concrete Dam.- Power House Cavern.- References.- Biographical Sketch.- 17. Vibration Problems: Theory.- Typical Problem Formulations.- Simultaneous Iteration Method.- General Remarks.- References.- 18. Vibration Problems: Applications.- Mode Superposition.- Applications.- References.- 19. Stability of Structures.- Static Stability Eigenproblems.- Traversing Critical Points.- References.- 20. Stability of Structures - Applications.- Concepts of Structural Stability and Criterion of Stability.- Formulation of the Stability Problem.- Applications.- Remarks.- References.- 21. Elastic Contact Problems.- Solution of the Elastic Contact Problem Using Analytical Methods.- Finite Element Analysis of Elastic Contact Problems.- Finite Element Modelling of Frictionless Contact Problems.- Finite Element Modelling of Elastic Contact Problems with Friction.- Finite Element Modelling of Dynamic Contact.- References.- Appendix 1.- 22. Fracture Mechanics.- Prel iminaries.- Fundamentals of Nonlinear Fracture Mechanics.- References.- 23. Analytical Solutions and Computational Methods in Plane Fracture.- Governing Equations of 20 Elasticity.- The Boundary Element Method.- The Schwartz-Newmann Alternating Technique.- Evaluation of Weight Functions.- Numerical Results.- Conclusions.- References.- 24. Methods for Analysis of Cracks in Three-Dimensional Solids.- List of Symbols.- Exact Solutions.- Approximate Methods.- Extraction of Stress-Intensity Factors.- Comparisons.- Concluding Remarks.- References.- 25. Recent Developments in Boundary Element Methods.- Infinitesimal Deformation of a Linear Elastic Solid.- Small-Strain Elasto-Plasticity.- Finite Strain E1asto-Plasticity.- Geometrically Nonlinear Behaviour of a Semi-Linear Solid.- Evaluation of Free Terms for the Integral Representation of Velocity Gradients.- Numerical Results for Linear Elasticity.- Numerical Implementation of Singular Integrals in Equation (74).- Numerical Results.- Closure.- References.- 26. The Discrete Element Method for the Analysis of Multiple Deformable/Rigid Bodies in Contact.- Dynamic Equilibrium Equations.- Time Integration Algorithm.- Contact Detection and Force Generation.- Discrete Fracture Model.- Applications.- Concluding Remarks.- References.- 27. A Review of Some Current Problems in Large Displacement Plasticity for Process Simulation.- Review of Finite Element Implementation of Plasticity.- Special Issues for Process Simulation Formulation.- Example Problems.- Conclusions.- References.- List of Symbols.- 28. A Primer on Probabilistic Structural Dynamics.- Response Characterist ics of Interest.- Response of Linear Systems.- Response of Nonlinear Systems.- Concluding Remarks.- References.- 29. Stochastic Linearization in Structural Dynamics.- Background on Alternative Methods of Random Vibration Analysis.- Concept and Applicability of the Method.- A Mathematical Formulation.- Performance Evaluation.- Some Possible or Expected Developments.- References.- 30. Digital Synthesis of Response-Design Spectrum Compatible Earthquake Records for Dynamic Analysis.- Response Spectrum.- Design Spectrum.- Algorithms of Digital Synthesis.- Concluding Remarks.- References.- 31. Stochastic Finite Element Expansion for Random Media.- Orthogonal Expansion.- Examples of Kernel Expansion.- Finite Element Formulation.- Numerical Example.- Summary.- Appendix I. Acknowledgement.- Appendix II. References.- Appendix III. Notation.- 32. Fem Analysis of Heat Exchangers.- Shell Tube Heat Exchangers.- Split Flow Exchanger.- Heat Exchanger With Phase Change.- Conclusions.- Nomenclature.- References.- 33. Conductive Convective Heat Transfer.- Nonlinear Transient Heat Conduction.- Fluid Flow and Heat Transfer.- Conclusions.- Nomenclature.- References.- 34. Knowledge Based Expert Systems for Finite Element Analysis.- Knowledge Based Expert Systems.- Problems to be Addressed by Finite Element Analysis Consultant.- A Framework for Finite Element Analysis Expert Systems.- Case Studies of Expert Systems for Finite Element Analysis.- References.- 35. Gravity Probe.- Experiment Description.- Structural Considerations.- Satellite System.- References.- Biographical Sketch.- Author Index.